Borussia Dortmund's first game after Jurgen Klopp announced his summer exit ended in a 3-0 win over Paderborn.
Paderborn picked up a crucial three points in their battle to avoid relegation after beating Augsburg 2-1.
Schalke's hopes of a top-four finish receded further after a goalless draw at Augsburg on Sunday.
Hertha Berlin took a potentially decisive step away from the Bundesliga's relegation zone with a 2-0 win over Paderborn.
Paderborn slipped into the bottom two of the Bundesliga after being held to a goalless draw at home by 10-man Hoffenheim on Saturday.
Augsburg's hopes of playing in Europe next season suffered a setback as they were beaten 2-0 at home by Mainz.
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